The problem probably lies in noise-shaping DSP techniques used by sigma-delta ADCs and DACs, which I personally strive to avoid. @uhoh, you'll never get virtually close even to 20-bit dynamic range (using real, read R2R temperature-compensated no-oversampling DACs) with any analog gear (2^20 is much much higher dynamic range than ~140dB which is about the limit of any analog gear).
If you want real, as colloquially called "analog" sound feel, use R2R DACs with no oversampling as well as so-called flash ADCs. Would be expensive as hell, but beats any analog gear in every possible way. Sigma-delta DACs, currently 90% of pro-audio market and close to 100% of consumer audio market are actually 1-bit DACs which run at "insane" frequencies like tens of MHz followed by a reconstruction filter (which is usually also quite poor quality) so they're obviously doing extreme oversampling to "make up" their 1-bit dynamic range with high "sampling rate". If anything 1-bit can be called "sampling", of course.
To get this close as we know them nowadays to real DACs they need some DSP processing, of which the crucial part is aggressive noise-shaping techniques moving most of the quantization noise (which obviously is extremely high here) to 30-40+ kHz range, which is supposed to being cut-off by the (low-pass) reconstruction filter.
But filters as well as switching elements (transistors) aren't ideal, and that's the actual problem. The delta-part of this kind of DACs/ADCs is briefly a feedback for the DSP processor. Everything above is a great simplification, but I hope it's understandable for people without advanced DSP background.
Even further, often those DACs are using just like 6-10 most significant bits of every sample of your PCM recording, they aren't able to reproduce more dynamic range on 1-bit output, even with their DSP processing. That's why noise-shaping gets even more important. Similar things are happening with sigma-delta ADCs, but it's also a huge simplification. Also speaking briefly, sigma-delta ADCs are much more difficult to replace than equivalent DACs.
Summarizing, some part of your (recording) chain is probably doing some crude noise-shaping, that's could be why you see some high-amplitude noise on the borderline of audible frequencies.